Battery knowledge · State estimation
Coulomb counting
Estimating state of charge by integrating the measured current over time. Simple and fast, but sensor offset accumulates, so it is corrected against the OCV–SOC curve at rest or fused with it in a Kalman filter. [1]
- Also called
- ampere-hour counting
- Relationship
- SOC(t) = SOC₀ − ∫ I dt / Q
Example
Integrate a discharge step
Starting at 80% SOC with a 5 Ah available capacity, an ideal 2 A discharge for 30 min removes 1 Ah and lowers SOC to 60%. This example takes discharge current as positive and ignores efficiency and sensor error.
Explore the graph
SOC rises with accumulated charge; depth of discharge falls by the same amount.
From 20% SOC, ideal full charge takes 48 min. Integration stops at 100%.
SOC = SOC₀ + ∫ I_charge dt / Q; DOD = 1 − SOC
Illustrative model. Current is positive into the cell. Constant capacity and 100% charge efficiency; no CC-CV taper.
Use in Lemonergy
Lemonergy Studio blocks
Connect SOC and voltage
The battery integrates charge and combines OCV with resistance.
Blocks to use
- Battery with SOC-dependent OCV
Stores charge and supplies terminal voltage
Inputs & settings
- capacityAh
- initialSoc
- emptyVoltageV / fullVoltageV
- resistanceOhm
- Electrical ports p and n
- Regulated CC/CV charger
Regulates current and voltage
Inputs & settings
- currentA
- voltageV
- cutoffCurrentA / cutoffHoldS
- Electrical ports p and n
- Electrical reference
Sets zero potential
Inputs & settings
- Connect p to reference net
This overview identifies the components to use. Follow the example in Lemonergy for their connections and settings.
- Inspect capacity, initial SOC and OCV endpoints.
- Compare OCV with terminal voltage.
Example. OCV endpoints of 300 and 420 V give 360 V at 50% SOC. Charging at 10 A through 0.08 Ω adds 0.8 V.
Observe. At unity coulombic efficiency, 10 A for 1 h adds ten percentage points to 100 Ah.
Internal model SOC is not an estimate of an unknown physical battery. OCV is linear and resistance fixed.
Open the Studio example →References & further reading
Technical references
- Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification
Gregory L. Plett · Journal of Power Sources · 2004
Technical reference · Battery charge balance, open-circuit voltage, ohmic loss, polarization dynamics and model identification; parameters require cell-specific data.
Further reading on this topic
These sources provide broader context; they are not presented as citations for every statement in this entry.
- Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation
Gregory L. Plett · Journal of Power Sources · 2004
Topic background · Model-based battery state-of-charge and parameter estimation with extended Kalman filtering, including uncertainty and model dependence.